Question

The half life period of a radioactive substance is $20$ days. The time taken for $\frac{7}{8}th$ of its original mass to disintegrate is:

• A. $58days$
• B. $59days$
• C. $60days$
• D. $61days$

Answer 1

The correct option is C $60days$

$t_{1/2}=20days$

Initial $=N_0$

Final amount left $=\frac{1}{8}{N}_0$

$ln\frac{N_0}{1/8N_0}=\left(\frac{0.693}{20}\right)t$

$t=60days$